Gamow-Teller unit cross sections for (t,He3) and (He3,t) reactions

The proportionality between differential cross sections at vanishing linear momentum transfer and Gamow-Teller transition strength, expressed in terms of the unit cross section (${\mathrm{\ensuremath{\sigma}\ifmmode \hat{}\else \^{}\fi{}}}_{\mathit{GT}}$), was studied as a function of target mass number for ($t$,$^{3}\mathrm{He}$) and ($^{3}\mathrm{He}$,$t$) reactions at $115A$ MeV and $140A$ MeV, respectively. Existing ($^{3}\mathrm{He}$,$t$) and ($t$,$^{3}\mathrm{He}$) data on targets with mass number $12\ensuremath{\leqslant}A\ensuremath{\leqslant}120$ were complemented with new and reevaluated ($t$,$^{3}\mathrm{He}$) data on proton, deuteron, $^{6}\mathrm{Li}$, and $^{12}\mathrm{C}$ targets. It was found that in spite of the small difference in beam energies between the two probes, the unit cross sections have a nearly identical and simple dependence on target mass number $A$, for $A\ensuremath{\geqslant}12$: ${\mathrm{\ensuremath{\sigma}\ifmmode \hat{}\else \^{}\fi{}}}_{\mathit{GT}}=109/{A}^{0.65}$. The factorization of the unit cross sections in terms of a kinematical factor, a distortion factor, and the strength of the effective spin-isospin transfer nucleus-nucleus interaction was investigated. Simple phenomenological functions depending on mass number $A$ were extracted for the latter two. By comparison with plane and distorted-wave Born approximation calculations, it was found that the use of a short-range approximation for knock-on exchange contributions to the transition amplitude results in overestimated cross sections for reactions involving the composite ($^{3}\mathrm{He}$,$t$) and ($t$,$^{3}\mathrm{He}$) probes.